The present invention relates generally to a method and apparatus for evaluating the resistivity of a borehole using a multi-array induction sonde, and more particularly, to a method and apparatus for evaluating the resistivity of invaded formations at high apparent dip angle.
It is important to the oil and gas industry to know the nature and characteristics of the various sub-surface formations penetrated by a borehole because the mere creation of the borehole usually does not provide sufficient information concerning the existence, depth location, quantity, etc., of oil and gas trapped in the formations. One commonly used tool is the induction logging sonde. Induction devices employ alternating currents in transmitter coils to set up an alternating magnetic field in the surrounding conductive formation. This changing magnetic field induces current loops in the formation that are detectable by a receiver coil in the induction sonde. The voltage detected at the receiver coil will vary inversely with the resistivity of the formation. U.S. Pat. Nos. 3,340,464; 3,147,429; 3,179,879; 3,056,917; and 4,472,684 are illustrative of typical prior art well logging devices which utilize the basic principles of induction logging.
The maximum entropy method has been utilized in the well logging industry to obtain inversions of instrumentally blurred and noisy data. U.S. Pat. No. 5,210,691 issued to Freedman et al., the disclosure of which is incorporated by reference into this specification, describes a maximum entropy method for inverting induction log data. The method involves setting up a series of thin earth layers and solving for the conductivity of each layer that closely produces the observed logs. The reconstructed thin layer sequence can be shown to be a close approximation to the actual formation. The maximum entropy method improves the resolution and accuracy of the estimated resistivity of the uninvaded virgin zone, R.sub.t. This method is exact only when there is no invasion of drilling fluids into the formation. The maximum entropy method inversion results in resistivities which are different from R.sub.t in the presence of invasion. A quasi-Newton algorithm based on a maximum entropy method Lagrangian functional has been applied to invert induction log data in dipping beds. See Gerald N. Minerbo, Inversion of Induction Logs in Dipping Beds, 1989 PROCEEDINGS FROM THE PROGRESS IN ELECTROMAGNETIC RESEARCH SYMPOSIUM 293-294. However, this algorithm is exact only when there is no invasion of drilling fluids into the dipping beds.
Evaluation of induction logs in highly deviated wells or in formations with high dip angle is complicated by the large volume of investigation of the induction logging tool. FIG. 1 shows in the vertical segment the focusing developed for vertical wells which concentrates the response within the layers (A). Referring to FIG. 2, when the hole is deviated, or when the beds dip with respect to the borehole, the focused response includes layers (B). FIG. 3 shows a computed multi-array induction log in a formation. The log on the right is computed at zero dip or deviation, showing excellent focusing using prior art processing techniques. The log on the left is computed at 70.degree. dip. As suggested by FIG. 2, the high dip angle log shows a blending of adjacent layers. The effect of dip on the induction log makes beds appear thicker, thin beds are more affected than thick beds, and resistive beds are more affected than conductive beds. The resistivity measurement is a blending of the adjacent layers.
U.S. Pat. No. 5,184,079 issued to Thomas D. Barber, the disclosure of which is incorporated by reference into this specification, is directed to a method and apparatus for eliminating the effects of apparent dip introduced in the induction log. Barber describes a dip correction algorithm, adapted to be used in association with a well logging truck computer which produces an induction log, for correcting an error introduced in the induction log by dip effect by means of inverse filters which are computed using log response functions derived from simple dipping formation models. The dip correction algorithm is exact only when there is no invasion of drilling fluids into the formation. None of the heretofore known methods which evaluate the resistivity of a formation also evaluate the resistivity of invaded formations at high apparent dip angle.